122 PROCEEDINGS OF THE AMERICAN ACADEMY. 



no slipping. If there is no slipping, then, in order that the stress at 

 the solid should be the same as when there is slipping, namely a-x, the 

 distance between the planes must be increased by 2 ju/o-, that is, twice 

 the coefficient of slip as defined by Maxwell. In the figure, then, the 

 distance P is equal to /a/o-. 



The investigation of the law of friction on a body at pressures smaller 

 than those at which Maxwell worked was taken up by Kundt and 

 Warburg,^ but without adequate means of measuring pressure. They 

 verified Maxwell's law, and concluded, both on theoretical grounds and 

 from their experimental data, that over a certain range of pressure the 

 coefficient of slip varies inversely as the density of the gas, and there- 

 fore, so long as Boyle's law holds, it varies inversely as the pressure. 

 Sutherland ^^ reached the same conclusion by a different method. If this 

 is true and /x is constant, then o-, as defined above, must be proportional 

 to the pressure. When the density of the gas has been so far reduced 

 that the molecules seldom collide in passing from one solid surface to 

 the other, then the friction is largely superficial or external, and one 

 would expect that at less densities the resistance offered to the 

 movement of the solid body would be well-nigh proportional to the 

 pressure. ^^ 



Maxwell's viscosity apparatus consisted, essentially, of a disk of glass 

 suspended with its plane horizontal and between two other larger fixed 

 parallel disks of glass. The middle disk performed oscillations in its 

 own plane. When the distance D, between the fixed and moving sur- 

 faces is small, Maxwell's formula for this apparatus becomes 



X-^=^ (I) 



Where X is the total logarithmic decrement, 



K is that due to the friction in the suspending fibre, and is a 

 constant. 



/A is the coefficient of viscosity of the gas. 



Z>, the distance between fixed and moving surfaces, 



c, a proportionality factor. 

 This is the formula only when slipping is not taken into account. 

 When slipping must be considered, as has been said above, the fixed 

 and moving surfaces may be considered removed fi-om each other by a 

 distance 2 /?, where /? is the coefficient of slip. 



9 Wicd. Ann, 158, 1876. 

 " Phil. Mag., [f,], 43, 1897. 

 " Kundt and Warburg, Wied. Ann., 158, 1876. 



